distributions-normal-cdf

Cumulative Distribution Function
===
[![NPM version][npm-image]][npm-url] [![Build Status][travis-image]][travis-url] [![Coverage Status][codecov-image]][codecov-url] [![Dependencies][dependencies-image]][dependencies-url]

> Normal distribution cumulative distribution function.

The cumulative distribution function for a normal random variable is

where mu is the mean and sigma > 0 is the standard deviation.

Installation

`` bash
$ npm install distributions-normal-cdf
`

For use in the browser, use browserify.

Usage

` javascript
var cdf = require( 'distributions-normal-cdf' );
`

#### cdf( x[, options] )

Evaluates the cumulative distribution function for the normal distribution. x may be either a number, an array, a typed array, or a matrix.

` javascript
var matrix = require( 'dstructs-matrix' ),
mat,
out,
x,
i;

out = cdf( 1 );
// returns ~0.841

x = [ -2, -1, 0, 1, 2 ];
out = cdf( x );
// returns [ ~0.0228, ~0.159, ~0.5, ~0.841, ~0.977 ]

x = new Float32Array( x );
out = cdf( x );
// returns Float64Array( [~0.0228,~0.159,~0.5,~0.841,~0.977] )

x = new Float32Array( 6 );
for ( i = 0; i < 6; i++ ) {
x[ i ] = i - 3;
}
mat = matrix( x, [3,2], 'float32' );
/*
[ -3 -2
-1 0
1 2 ]
*/

out = cdf( mat );
/*
[ ~0.0013 ~0.0228
~0.159 ~0.5
~0.841 ~0.977 ]
*/
`

The function accepts the following options:

* __mu__: mean. Default: 0.
* __sigma__: standard deviation. Default: 1.
* __accessor__: accessor function for accessing array values.
* __dtype__: output typed array or matrix data type. Default: float64.
* __copy__: boolean indicating if the function should return a new data structure. Default: true.
* __path__: deepget/deepset key path.
* __sep__: deepget/deepset key path separator. Default: '.'.

A normal distribution is a function of two parameters: mu(mean) and sigma(standard deviation). By default, mu is equal to 0 and sigma is equal to 1. To adjust either parameter, set the corresponding option.

` javascript
var x = [ -2, -1, 0, 1, 2 ];

var out = cdf( x, {
'mu': 3,
'sigma': 10
});
// returns [ ~0.309, ~0.345, ~0.382, ~0.421, ~0.46 ]
`

For non-numeric arrays, provide an accessor function for accessing array values.

` javascript
var data = [
[0,-2],
[1,-1],
[2,0],
[3,1],
[4,2],
];

function getValue( d, i ) {
return d[ 1 ];
}

var out = cdf( data, {
'accessor': getValue
});
// returns [ ~0.0228, ~0.159, ~0.5, ~0.841, ~0.977 ]
`


To deepset an object array, provide a key path and, optionally, a key path separator.

` javascript
var data = [
{'x':[0,-2]},
{'x':[1,-1]},
{'x':[2,0]},
{'x':[3,1]},
{'x':[4,2]},
];

var out = cdf( data, {
'path': 'x/1',
'sep': '/'
});
/*
[
{'x':[0,~0.0228]},
{'x':[1,~0.159]},
{'x':[2,~0.5]},
{'x':[3,~0.841]},
{'x':[4,~0.977]},
]
*/

var bool = ( data === out );
// returns true
`

By default, when provided a typed array or matrix, the output data structure is float64 in order to preserve precision. To specify a different data type, set the dtype option (see matrix for a list of acceptable data types).

` javascript
var x, out;

x = new Float64Array( [-2,-1,0,1,2] );

out = cdf( x, {
'dtype': 'float32'
});
// returns Float32Array( [~0.0228,~0.159,~0.5,~0.841,~0.977] )

// Works for plain arrays, as well...
out = cdf( [-2,-1,0,1,2], {
'dtype': 'float32'
});
// returns Float32Array( [~0.0228,~0.159,~0.5,~0.841,~0.977] )
`

By default, the function returns a new data structure. To mutate the input data structure (e.g., when input values can be discarded or when optimizing memory usage), set the copy option to false.

` javascript
var bool,
mat,
out,
x,
i;

x = [ -2, -1, 0, 1, 2 ];

out = cdf( x, {
'copy': false
});
// returns [ ~0.0228, ~0.159, ~0.5, ~0.841, ~0.977 ]

bool = ( x === out );
// returns true

x = new Float32Array( 6 );
for ( i = 0; i < 6; i++ ) {
x[ i ] = i - 3 ;
}
mat = matrix( x, [3,2], 'float32' );
/*
[ -3 -2
-1 0
1 2 ]
*/

out = cdf( mat, {
'copy': false
});
/*
[ ~0.0013 ~0.0228
~0.159 ~0.5
~0.841 ~0.977 ]
*/

bool = ( mat === out );
// returns true
`

Notes

* If an element is __not__ a numeric value, the evaluated cumulative distribution function is NaN.

` javascript
var data, out;

out = cdf( null );
// returns NaN

out = cdf( true );
// returns NaN

out = cdf( {'a':'b'} );
// returns NaN

out = cdf( [ true, null, [] ] );
// returns [ NaN, NaN, NaN ]

function getValue( d, i ) {
return d.x;
}
data = [
{'x':true},
{'x':[]},
{'x':{}},
{'x':null}
];

out = cdf( data, {
'accessor': getValue
});
// returns [ NaN, NaN, NaN, NaN ]

out = cdf( data, {
'path': 'x'
});
/*
[
{'x':NaN},
{'x':NaN},
{'x':NaN,
{'x':NaN}
]
*/
`

Examples

` javascript
var cdf = require( 'distributions-normal-cdf' ),
matrix = require( 'dstructs-matrix' );

var data,
mat,
out,
tmp,
i;

// Plain arrays...
data = new Array( 10 );
for ( i = 0; i < data.length; i++ ) {
data[ i ] = i - 5;
}
out = cdf( data );

// Object arrays (accessors)...
function getValue( d ) {
return d.x;
}
for ( i = 0; i < data.length; i++ ) {
data[ i ] = {
'x': data[ i ]
};
}
out = cdf( data, {
'accessor': getValue
});

// Deep set arrays...
for ( i = 0; i < data.length; i++ ) {
data[ i ] = {
'x': [ i, data[ i ].x ]
};
}
out = cdf( data, {
'path': 'x/1',
'sep': '/'
});

// Typed arrays...
data = new Float32Array( 10 );
for ( i = 0; i < data.length; i++ ) {
data[ i ] = i - 5;
}
out = cdf( data );

// Matrices...
mat = matrix( data, [5,2], 'float32' );
out = cdf( mat );

// Matrices (custom output data type)...
out = cdf( mat, {
'dtype': 'uint8'
});
`

To run the example code from the top-level application directory,

` bash
$ node ./examples/index.js
`

Tests

$3

Unit tests use the Mocha test framework with Chai assertions. To run the tests, execute the following command in the top-level application directory:

` bash
$ make test
`

All new feature development should have corresponding unit tests to validate correct functionality.

$3

This repository uses Istanbul as its code coverage tool. To generate a test coverage report, execute the following command in the top-level application directory:

` bash
$ make test-cov
`

Istanbul creates a ./reports/coverage directory. To access an HTML version of the report,

` bash
$ make view-cov
``

---

License

MIT license.

Copyright

Copyright © 2015. The Compute.io Authors.

[npm-image]: http://img.shields.io/npm/v/distributions-normal-cdf.svg
[npm-url]: https://npmjs.org/package/distributions-normal-cdf

[travis-image]: http://img.shields.io/travis/distributions-io/normal-cdf/master.svg
[travis-url]: https://travis-ci.org/distributions-io/normal-cdf

[codecov-image]: https://img.shields.io/codecov/c/github/distributions-io/normal-cdf/master.svg
[codecov-url]: https://codecov.io/r/distributions-io/normal-cdf?branch=master

[dependencies-image]: http://img.shields.io/david/distributions-io/normal-cdf.svg
[dependencies-url]: https://david-dm.org/distributions-io/normal-cdf

[dev-dependencies-image]: http://img.shields.io/david/dev/distributions-io/normal-cdf.svg
[dev-dependencies-url]: https://david-dm.org/dev/distributions-io/normal-cdf

[github-issues-image]: http://img.shields.io/github/issues/distributions-io/normal-cdf.svg
[github-issues-url]: https://github.com/distributions-io/normal-cdf/issues